Acceleration Due to Gravity: Super Mario Brothers

Abstract

The
purpose of this analysis is to determine the evolution of gravity in
the Mario video game series as video game hardware increases.

Introduction

Gravity is force which is responsible for keeping us on the ground. It is
also the force that prohibits us from jumping 50 feet in the air. However,
in Mario's world, gravity does not quite work that way. Mario is able to
jump 5 times his height and fall with accelerations that would be deadly
to humans.

We will find Mario's acceleration due to gravity by using the formula

s = s0 + v0t + ½ at2

where s is the distance he falls, s0 is his initial distance, which
is 0, v0 is his initial vertical velocity, which is also 0, a is
his acceleration due to gravity, and t is the time it takes for him to fall.
When we solve this formula for a, we get

a = 2s / t2

Procedure

Record video clips of Mario falling from a ledge in the following games:

Super Mario Bros 1, 2 & 3, for NES

Super Mario World for SNE

Super Mario 64 for N64

Super Mario Sunshine GCN

Super Paper Mario for Wii

Watch the clip in Quicktime Video Player and use the frame by frame option
to determine the number of frames it took Mario to fall. Also using Quicktime,
the FPS, or frames per second, of each video must be found.

Take a screen shot of Mario standing next to the ledge. This Screen shot will
be used to determine the distance of the fall.

Analysis

First, you must find the time it took Mario to fall from the edge of the ledge
to the ground in each game. To do this, we opened each clip in Quicktime movie
player, and using the frame by frame option, found the total number of frames
it took Mario to fall. We then used the formula:

Time = (Number of Frames) / (Frame Rate)

To find the time of each of Mario's falls. Once we knew the time, we needed
to figure out the distance Mario fell in each game. We used a screen shot
of Mario next to the ledge he fell from in each game, and found the height
of Mario and the ledge in pixels. According to Wikipedia, Mario is "a little over five feet tall.", so we used 5 feet, or 1.524 meters, as Mario's height. We used the formula:

HeightMario[m] / HeightMario[pixels] = Distance[m] / Distance[pixels]

Distance = (HeightMario[m] / HeightMario[pixels]) x Distance[pixels]

Once we had the distance Mario fell in each instance, we were able to use the formula

s = s0 + v0t + ½ at2

to find Mario's acceleration in each game. Mario was in free fall in each
case, so this acceleration was equal to gravity. His initial velocity was
0, as was his initial position. Our results in m/s2 as well
as in multiples of g are outlined in the table below.

Game

Frames

Time(s)

Height of Mario(pixels)

Distance of Fall(pixels)

Distance of Fall(m)

Acceleration(m/s2)

Acceleration(g)

Super Mario Bros.

15

0.5

39

292

11.4

91.28

9.31

Super Mario Bros. 2

12

0.4

45

255

8.6

107.95

11

Super Mario Bros. 3

15

0.5

35

265

11.5

92.31

9.42

Super Mario World

15

0.5

38

193

7.7

61.92

6.32

Super Mario 64

10

0.33

86

217

3.8

69.22

7.06

Super Mario Sunshine

23

0.77

119

988

12.7

43.05

4.4

Super Paper Mario

12

0.4

288

748

4

49.47

5.05

Finally, we graphed the acceleration due to gravity in each game as the bit
rate of the graphics processor increased. Since Super Mario Bros. 1, 2, and
3 were from the same console, we took an average of the three values. Also,
the Nintendo Wii never clearly defined its bit rate, but sources say that it
is 96 Bits, which is actually less than that of the Nintendo GameCube. As for
the other systems, the NES is an 8 Bit system, the SNES is 16 bit, the N64 is
64 Bit, and the GCN is 128 Bit. We set a power fit to this graph, and the result
is shown below.

Conclusion

We determined that, generally speaking, the gravity in each Mario game, as
game hardware has increased, is getting closer to the true value of gravity
on earth of 9.8 m/s2. However, gravity, even on the newest consoles,
is still extreme. According to Wikipedia, a typical person can withstand 5 g
before losing consciousness, and all but the very latest of Mario games have
gravity greater than this. Also, with gravity that great, it is a wonder Mario
can perform such feats as leaping almost 5 times his own body height!

Sources of Error

The primary source of error in this experiment would be the assumption that
Mario is 5 feet tall, and that his height stays constant in each game. In most
Mario games, he can become bigger by consuming mushrooms or other powerup objects,
and the 5 foot height may be referring to this state. Also, in the 3D Mario
games, the camera angle was always angled down, so when measuring the height
of Mario and the ledge, this angle caused the measured distance to be different
than the actual distance.